Data Assimilating B-splines for Model-based Regularization in Ultrasound Vector Flow Imaging

This work aims to investigate the benefits of incorporating fluid dynamic models into ultrasound vector flow imaging through a novel data assimilation framework using tensor product B-splines for model-based regularization.

A variational data assimilation method was developed using tensor product B-splines with the goal of solving high-dimensional regularization problems governed by the Navier-Stokes equations. The method was implemented in an open-source library and validated across three experimental setups: in silico using a computational fluid dynamics phantom, in vitro using a pulsatile flow phantom with particle imaging velocimetry and in vivo using 4-D ultrasound compared with magnetic resonance imaging.

The proposed method outperformed conventional smoothing techniques and matched the performance of state-of-the-art regularization approaches. In silico tests showed improved noise suppression and lower root mean squared error. In vitro experiments demonstrated accurate reconstruction of flow features and gradient-based metrics. In vivo comparisons revealed good agreement with magnetic resonance imaging in high-velocity regions and successful reconstruction in dropout zones.

The data assimilation approach using B-splines and fluid dynamic constraints enables efficient and accurate reconstruction of 4-D flow fields in ultrasound vector flow imaging. It offers a promising solution for bedside clinical applications, balancing noise suppression and resolution while leveraging physical models for robust flow estimation.